Multi-objective optimal power flow using quasi-oppositional teaching learning based optimization

This paper describes teaching learning based optimization (TLBO) algorithm to solve multi-objective optimal power flow (MOOPF) problems while satisfying various operational constraints. To improve the convergence speed and quality of solution, quasi-oppositional based learning (QOBL) is incorporated in original TLBO algorithm. The proposed quasi-oppositional teaching learning based optimization (QOTLBO) approach is implemented on IEEE 30-bus system, Indian utility 62-bus system and IEEE 118-bus system to solve four different single objectives, namely fuel cost minimization, system power loss minimization and voltage stability index minimization and emission minimization; three bi-objectives optimization namely minimization of fuel cost and transmission loss; minimization of fuel cost and L-index and minimization of fuel cost and emission and one tri-objective optimization namely fuel cost, minimization of transmission losses and improvement of voltage stability simultaneously. In this article, the results obtained using the QOTLBO algorithm, is comparable with those of TLBO and other algorithms reported in the literature. The numerical results demonstrate the capabilities of the proposed approach to generate true and well-distributed Pareto optimal non-dominated solutions of the multi-objective OPF problem. The simulation results also show that the proposed approach produces better quality of the individual as well as compromising solutions than other algorithms.     

Particle swarm optimization with an aging leader and challengers algorithm for the solution of optimal power flow problem

Solution of optimal power flow (OPF) problem aims to optimize a selected objective function such as fuel cost, active power loss, total voltage deviation (TVD) etc. via optimal adjustment of the power system control variables while at the same time satisfying various equality and inequality constraints. In the present work, a particle swarm optimization with an aging leader and challengers (ALC-PSO) is applied for the solution of the OPF problem of power systems. The proposed approach is examined and tested on modified IEEE 30-bus and IEEE 118-bus test power system with different objectives that reflect minimization of fuel cost or active power loss or TVD. The simulation results demonstrate the effectiveness of the proposed approach compared with other evolutionary optimization techniques surfaced in recent state-of-the-art literature. Statistical analysis, presented in this paper, indicates the robustness of the proposed ALC-PSO algorithm.     

Optimal reactive power dispatch for real power loss minimization and voltage stability enhancement using Artificial Bee Colony Algorithm

Reactive Power Dispatch (RPD) plays important role in power system reliability and security. This paper proposes the Optimal Reactive Power Dispatch (ORPD) for real power loss minimization, voltage deviation minimization and voltage stability enhancement using Artificial Bee Colony (ABC) Algorithm. ORPD is a mixed integer nonlinear optimization problem which includes both continuous and discrete control variables. The ABC algorithm is used to find the setting of control variables such as generator voltage magnitude, tap position of tap changing transformer and reactive power output of the compensation devices. The proposed algorithm is tested on IEEE 30 and 57 bus systems, Simulation results show that the proposed approach converges to better solutions and much faster than the earlier reported approaches in the literature. The optimization strategy is general and can be used to solve other power system optimization problems.     

Congestion management by determining optimal location of series FACTS devices using hybrid bacterial foraging and Nelder–Mead algorithm

In this paper, the Thyristor-Controlled Series-Compensated (TCSC) devices are located for congestion management in the power system by considering the non-smooth fuel cost function and penalty cost of emission. For this purpose, it is considered that the objective function of the proposed optimal power flow (OPF) problem is minimizing fuel and emission penalty cost of generators. A hybrid method that is the combination of the bacterial foraging (BF) algorithm with Nelder–Mead (NM) method (BF-NM) is employed to solve the OPF problems. The optimal location of the TCSC devices are then determined for congestion management. The size of the TCSC is obtained by using of the BF-NM algorithm to minimize the cost of generation, cost of emission, and cost of TCSC. The simulation results on IEEE 30-bus, modified IEEE 30-bus and IEEE 118-bus test system confirm the efficiency of the proposed method for finding the optimal location of the TCSC with non-smooth non-convex cost function and emission for congestion management in the power system. In addition, the results clearly show that a better solution can be achieved by using the proposed OPF problem in comparison with other intelligence methods.     

Chaotic krill herd algorithm for optimal reactive power dispatch considering FACTS devices

Conventionally, optimal reactive power dispatch (ORPD) is described as the minimization of active power transmission losses and/or total voltage deviation by controlling a number of control variables while satisfying certain equality and inequality constraints. This article presents a newly developed meta-heuristic approach, chaotic krill herd algorithm (CKHA), for the solution of the ORPD problem of power system incorporating flexible AC transmission systems (FACTS) devices. The proposed CKHA is implemented and its performance is tested, successfully, on standard IEEE 30-bus test power system. The considered power system models are equipped with two types of FACTS controllers (namely, thyristor controlled series capacitor and thyristor controlled phase shifter). Simulation results indicate that the proposed approach yields superior solution over other popular methods surfaced in the recent state-of-the-art literature including chaos embedded few newly developed optimization techniques. The obtained results indicate the effectiveness for the solution of ORPD problem of power system considering FACTS devices. Finally, simulation is extended to some large-scale power system models like IEEE 57-bus and IEEE 118-bus test power systems for the same objectives to emphasis on the scalability of the proposed CKHA technique. The scalability, the robustness and the superiority of the proposed CKHA are established in this paper.     

Reactive power and voltage control based on general quantum genetic algorithms

This paper presents an improved evolutionary algorithm based on quantum computing for optimal steady-state performance of power systems. However, the proposed general quantum genetic algorithm (GQ-GA) can be applied in various combinatorial optimization problems. In this study the GQ-GA determines the optimal settings of control variables, such as generator voltages, transformer taps and shunt VAR compensation devices for optimal reactive power and voltage control of IEEE 30-bus and 118-bus systems. The results of GQ-GA are compared with those given by the state-of-the-art evolutionary computational techniques such as enhanced GA, multi-objective evolutionary algorithm and particle swarm optimization algorithms, as well as the classical primal-dual interior-point optimal power flow algorithm. The comparison demonstrates the ability of the GQ-GA in reaching more optimal solutions.     

基于AMFOA考虑主客观因素的配电网多目标规划

针对配电网重构的多目标优化及方案决策问题,提出一种基于自适应多种群果蝇算法(AMFOA)并考虑主客观因素的多目标两级优化方法.第一级优化采用自适应多种群果蝇算法对网络结构进行迭代优化,通过协调不同指标得到一组帕累托非支配解.第二级优化引入AHP-CRITIC算法完成每个非支配解的主客观综合评价,结合TOPSIS法确定最...     

基于自变量简约的大规模稀疏多目标优化

现有的大多数进化算法在求解大规模优化问题时性能会随决策变量维数的增长而下降。通常,多目标优化的Pareto有效解集是自变量空间的一个低维流形,该流形的维度远小于自变量空间的维度。鉴于此,提出一种基于自变量简约的多目标进化算法求解大规模稀疏多目标优化问题。该算法通过引入局部保持投影降维,保留原始自变量空间中的局部近邻关系,并设计一个归档集,将寻找到的非劣解存入其中进行训练,以提高投影的准确性。将该算法与四种流行的多目标进化算法在一系列测试问题和实际应用问题上进行了比较。实验结果表明,所提算法在解决稀疏多目标问题上具有较好的效果。因此,通过自变量简约能降低问题的求解难度,提高算法的搜索效率,在解决大规模稀疏多目标问题方面具有显著的优势。     

A modified MOEA/D approach to the solution of multi-objective optimal power flow problem

This study presents a modified multi-objective evolutionary algorithm based decomposition (MOEA/D) approach to solve the optimal power flow (OPF) problem with multiple and competing objectives. The multi-objective OPF considers the total fuel cost, the emissions, the power losses and the voltage magnitude deviations as the objective functions. In the proposed MOEA/D, a modified Tchebycheff decomposition method is introduced as the decomposition approach in order to obtain uniformly distributed Pareto-Optimal solutions on each objective space. In addition, an efficiency mixed constraint handling mechanism is introduced to enhance the feasibility of the final Pareto solutions obtained. The mechanism employs both repair strategy and penalty function to handle the various complex constraints of the MOOPF problem. Furthermore, a fuzzy membership approach to select the best compromise solution from the obtained Pareto-Optimal solutions is also integrated. The standard IEEE 30-bus test system with seven different cases is considered to verify the performance of the proposed approach. The obtained results are compared with those in the literatures and the comparisons confirm the effectiveness and the performance of the proposed algorithm.     

Comprehensive learning particle swarm optimization for reactive power dispatch

Reactive power dispatch (RPD) is an optimization problem that reduces grid congestion by minimizing the active power losses for a fixed economic power dispatch. RPD reduces power system losses by adjusting the reactive power control variables such as generator voltages, transformer tap-settings and other sources of reactive power such as capacitor banks and provides better system voltage control, resulting in an improved voltage profile, system security, power transfer capability and over all system operation. In this paper, RPD problem is solved using particle swarm optimization (PSO). To overcome the drawback of premature convergence in PSO, a learning strategy is introduced in PSO, and this approach called, comprehensive learning particle swarm optimization (CLPSO) is also applied to this problem and a comparison of results is made between these two. Three different test cases have been studied such as minimization of real power losses, improvement of voltage profile and enhancement of voltage stability through a standard IEEE 30-bus and 118-bus test systems and their results have been reported. The study results show that the approaches developed are feasible and efficient.     

Fuzzy-Pareto-dominance driven possibilistic model based planning of electrical distribution systems using multi-objective particle swarm optimization

This paper presents a fuzzy-Pareto dominance driven possibilistic model based planning of electrical distribution systems using multi-objective particle swarm optimization (MOPSO). This multi-objective planning model captures the possibilistic variations of the system loads using a fuzzy triangular number. The MOPSO based on the Pareto-optimality principle is used to obtain a set of non-dominated solutions representing different network structures under uncertainties in load demands and these non-dominated solutions are stored in an elite archive of limited size. Normally, choosing the candidate non-dominated solutions to be retained in the elite archive while maintaining the quality of the Pareto-approximation front as well as maintaining the diversity of solutions on this front is very much computationally demanding. In this paper, the principles of fuzzy Pareto-dominance are used to find out and rank the non-dominated solutions on the Pareto-approximation front. This ranking in turn is used to maintain the elite archive of limited size by discarding the lower ranked solutions. The two planning objectives are: (i) minimization of total installation and operational cost and (ii) minimization of risk factor. The risk factor is defined as a function of an index called contingency-load-loss index (CLLI), which captures the effect of load loss under contingencies, and the degree of network constraint violations. The minimization of the CLLI improves network reliability. The network variables that are optimized are: (i) number of feeders and their routes, and (ii) number and locations of sectionalizing switches. An MOPSO (developed by the authors), based on a novel technique for the selection and assignment of leaders/guides for efficient search of non-dominated solutions, is used as the optimization tool. The proposed planning approach is validated on a typical 100-node distribution system. Performance comparisons between the planning approaches with the possibilistic and deterministic load models are provided highlighting the relative merits and demerits. It is also verified that the proposed solution ranking scheme based on the fuzzy-Pareto dominance is very much better from both quality and computational burden point of view in comparison with the other well-known archive truncation techniques based on clustering and solution density measurement etc.     

Multi-objective optimization algorithms applied to the class integration and test order problem

In the context of object-oriented software, a common problem is the determination of test orders for the integration test of classes, known as the class integration and test order (CITO) problem. The existing approaches, based on graphs, usually generate solutions that are sub-optimal, and do not consider the different factors and measures that can affect the construction of stubs. To overcome this limitation, solutions based on genetic algorithms (GA) have presented promising results. However, the determination of a cost function, which is able to generate the best solution, is not always a trivial task, mainly for complex systems. Therefore, to better represent the CITO problem, we introduce, in this paper, a multi-objective optimization approach, to generate a set of good solutions that achieve a balanced compromise between the different measures (objectives). Three different multi-objective optimization algorithms (MOA) were implemented: Pareto ant colony, multi-objective Tabu search and non-dominated sorting GA. The approach is applied to real programs and the obtained results allow comparison with the simple GA approach and evaluation of the different MOA.     

Developing a multi-objective,multi-item inventory model and three algorithms for its solution

We develop a multi-objective model in a multi-product inventory system.The proposed model is a joint replenishment problem(JRP) that has two objective functions.The first one is minimization of total ordering and inventory holding costs,which is the same objective function as the classic JRP.To increase the applicability of the proposed model,we suppose that transportation cost is independent of time,is not a part of holding cost,and is calculated based on the maximum of stored inventory,as is the case in many real inventory problems.Thus,the second objective function is minimization of total transportation cost.To solve this problem three efficient algorithms are proposed.First,the RAND algorithm,called the best heuristic algorithm for solving the JRP,is modified to be applicable for the proposed problem.A multi-objective genetic algorithm(MOGA) is developed as the second algorithm to solve the problem.Finally,the model is solved by a new algorithm that is a combination of the RAND algorithm and MOGA.The performances of these algorithms are then compared with those of the previous approaches and with each other,and the findings imply their ability in finding Pareto optimal solutions to 3200 randomly produced problems.     

多种群协同进化算法在经济调度中的应用

为解决同时考虑环保要求、发电费用等多个目标的经济调度问题,基于生态系统中不同物种间的互利共生现象,提出一种多种群共生进化优化(SMSO)算法。对一个30节点IEEE系统进行计算,结果显示SMSO算法在获得最优Pareto解集、降低计算复杂度、提高收敛效率等方面具有较大的优越性。     

Multi-objective optimization of machining and micro-machining processes using non-dominated sorting teaching–learning-based optimization algorithm

Selection of optimum machining parameters is vital to the machining processes in order to ensure the quality of the product, reduce the machining cost, increasing the productivity and conserve resources for sustainability. Hence, in this work a posteriori multi-objective optimization algorithm named as Non-dominated Sorting Teaching–Learning-Based Optimization (NSTLBO) is applied to solve the multi-objective optimization problems of three machining processes namely, turning, wire-electric-discharge machining and laser cutting process and two micro-machining processes namely, focused ion beam micro-milling and micro wire-electric-discharge machining. The NSTLBO algorithm is incorporated with non-dominated sorting approach and crowding distance computation mechanism to maintain a diverse set of solutions in order to provide a Pareto-optimal set of solutions in a single simulation run. The results of the NSTLBO algorithm are compared with the results obtained using GA, NSGA-II, PSO, iterative search method and MOTLBO and are found to be competitive. The Pareto-optimal set of solutions for each optimization problem is obtained and reported. These Pareto-optimal set of solutions will help the decision maker in volatile scenarios and are useful for real production systems.     

Vehicle power train optimization using multi-objective bird swarm algorithm

In this paper, a multi-objective bird swarm algorithm (MOBSA) is proposed to cope with multi-objective optimization problems. The algorithm is explored based on BSA which is an evolutionary algorithm suitable for single objective optimization. In this paper, non-dominated sorting approach is used to distinguish optimal solutions and parallel coordinates is applied to evaluate the distribution density of non-dominated solution and further update the external archive when it is full to overflowing, which ensure faster convergence and more widespread of Pareto front. Then, the MOBSA is adopted to optimize benchmark problems. The results demonstrate that MOBSA gets better performance compared with NSGA-II and MOPSO. Since a vehicle power train problem could be treated as a typical multi-objective optimization problem with constraints, with integration of constrained non-dominated solution, MOBSA is adopted to acquire optimal gear ratios and optimize vehicle power train. The results compared with other popular algorithm prove the proposed algorithm is more suitable for constrained multi-objective optimization problem in engineering field.

     

Application of firefly algorithm for multi-stage transmission expansion planning with adequacy-security considerations in deregulated environments

Electric energy is the most popular form of energy because it can be transported easily at high efficiency and reasonable cost. Nowadays the real-world electric power systems are large-scale and highly complex interconnected transmission systems. The transmission expansion planning (TEP) problem is a large-scale optimization, complicated and nonlinear problem that the number of candidate solutions increases exponentially with system size. Investment cost, reliability (both adequacy and security), and congestion cost are considered in this optimization. To overcome the difficulties in solving the non-convex and mixed integer nature of this optimization problem, this paper offers a firefly algorithm (FA) to solve this problem. In this paper it is shown that FA, like other heuristic optimization algorithms, can solve the problem in a better manner compare with other methods such genetic algorithm (GA), particle swarm optimization (PSO), Simulated Annealing (SA) and Differential Evolution (DE). To show the feasibility of proposed method, applied model has been considered in IEEE 24-Bus, IEEE 118-Bus and Iran 400-KV transmission grid case studies for TEP problem in both adequacy and security modes. The obtained results show the capability of the proposed method. A comprehensive analysis of the GA, PSO, SA and DE with proposed method is also presented.     

Application and comparison of computational intelligence techniques for optimal location and parameter setting of UPFC

Unified power flow controller (UPFC) is one of the most effective flexible AC transmission systems (FACTS) devices for enhancing power system security. However, to what extent the performance of UPFC can be brought out, it highly depends upon the location and parameter setting of this device in the system. This paper presents a new approach based on computational intelligence (CI) techniques to find out the optimal placement and parameter setting of UPFC for enhancing power system security under single line contingencies (N?1 contingency). Firstly, a contingency analysis and ranking process to determine the most severe line outage contingencies, considering lines overload and bus voltage limit violations as a performance index, is performed. Secondly, a relatively new evolutionary optimization technique, namely: differential evolution (DE) technique is applied to find out the optimal location and parameter setting of UPFC under the determined contingency scenarios. To verify our proposed approach and for comparison purposes, simulations are performed on an IEEE 14-bus and an IEEE 30-bus power systems. The results, we have obtained, indicate that DE is an easy to use, fast, robust and powerful optimization technique compared with genetic algorithm (GA) and particle swarm optimization (PSO). Installing UPFC in the optimal location determined by DE can significantly enhance the security of power system by eliminating or minimizing the number of overloaded lines and the bus voltage limit violations.     

基于决策变量关系的动态多目标优化算法

动态多目标优化问题(DMOPs)需要进化算法跟踪不断变化的Pareto最优前沿,从而在检测到环境变化时能够及时有效地做出响应.为了解决上述问题,提出一种基于决策变量关系的动态多目标优化算法.首先,通过决策变量对收敛性和多样性贡献大小的检测机制将决策变量分为收敛性相关决策变量(CV)和多样性相关决策变量(DV),对不同类型决策变量采用不同的优化策略;其次,提出一种局部搜索多样性维护机制,使个体在Pareto前沿分布更加均匀;最后,对两部分产生的组合个体进行非支配排序构成新环境下的种群.为了验证DVR的性能,将DVR与3种动态多目标优化算法在15个基准测试问题上进行比较,实验结果表明, DVR算法相较于其他3种算法表现出更优的收敛性和多样性.     

Multi-objective based on parallel vector evaluated particle swarm optimization for optimal steady-state performance of power systems

In this paper the state-of-the-art extended particle swarm optimization (PSO) methods for solving multi-objective optimization problems are represented. We emphasize in those, the co-evolution technique of the parallel vector evaluated PSO (VEPSO), analysed and applied in a multi-objective problem of steady-state of power systems. Specifically, reactive power control is formulated as a multi-objective optimization problem and solved using the parallel VEPSO algorithm. The results on the IEEE 30-bus test system are compared with those given by another multi-objective evolutionary technique demonstrating the advantage of parallel VEPSO. The parallel VEPSO is also tested on a larger power system this with 136 busses.